Finite Group Databasebeta

← C3×#71753 #11774831

Subgroups — C3×#71753 #11774831

Order 1152.

549 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#529C211yesmaximal, characteristic
2C3×#4925C211yesmaximal, characteristic, complemented
3C3×#4924C211yesmaximal, characteristic, complemented
4C3×#4535C212yesmaximal, complemented
5C3×D4⋊(C3⋊C8)C212yesmaximal, complemented
6C3×#1495—31nomaximal
7#71753C311yesmaximal, characteristic, direct product factor
8C32×#126—21no—
9C32×#125C411yescharacteristic
10C32×#124C411yescharacteristic
11C32×#123—21no—
12C32×C22⋊Q8C411yescharacteristic
13C32×#121C411yescharacteristic
14C32×C4×Q8C2211yescharacteristic
15C32×C4×D4—21no—
16C32×C4×D4C2211yescharacteristic
17C32×#117—21no—
18C2×C32×C42C2211yescharacteristic
19C2×C3×#208—21no—
20C3×#830—21no—
21C3×C4⋊(C3⋊C8)—21no—
22C3×C4⋊(C3⋊C8)—21no—
23C3×C4⋊(C3⋊C8)C2212yes—
24C3×C4×C3⋊C8C2212yes—
25C3×#529—21no—
26C3×#529D311yescharacteristic
27C3×#529C2×C311yescharacteristic
28C3×#431—31no—
29C3×#423—31no—
30#4925C2×C311yescharacteristic, complemented
31#4924C2×C311yescharacteristic, complemented
32C3×Q8⋊C8—32no—
33C3×D4⋊C8—32no—
34#4535C2×C312yescomplemented
35D4⋊(C3⋊C8)C2×C312yescomplemented
36C2×C32×Q8C2×C411yescharacteristic
37C2×C32×D4—21no—
38C2×C32×D4C2×C411yescharacteristic
39C22×C32×C4—21no—
40C22×C32×C4C2×C411yescharacteristic
41C22×C32×C4D411yescharacteristic
42C22×C32×C4D411yescharacteristic
43C32×C4⋊C4—21no—
44C32×C4⋊C4—21no—
45C32×C4⋊C4—21no—
46C32×C4⋊C4—21no—
47C32×C4⋊C4C2×C411yescharacteristic
48C32×C4⋊C4C2×C411yescharacteristic
49C32×C22⋊C4—21no—
50C32×C22⋊C4—21no—
51C32×C22⋊C4—21no—
52C32×C22⋊C4—21no—
53C32×C22⋊C4—21no—
54C32×C42—21no—
55C32×C42C2×C411yescharacteristic
56C32×C42D411yescharacteristic
57C32×C42D411yescharacteristic
58C32×C42C2311yescharacteristic
59C3×#208—42no—
60C2×C3×C3⋊C8—22no—
61C2×C3×C3⋊C8—22no—
62#1495—31noSylow
63C2×C3×M16—61no—
64C3×#126—22no—
65C3×#126—21no—
66C3×#126—21no—
67C3×#125—21no—
68C3×#125Dic311yescharacteristic
69C3×#125C3×C411yescharacteristic
70C3×#124—21no—
71C3×#124Dic311yescharacteristic
72C3×#124C3×C411yescharacteristic
73C3×#123—22no—
74C3×#123—21no—
75C3×#123—21no—
76C3×C22⋊Q8—21no—
77C3×C22⋊Q8Dic311yescharacteristic
78C3×C22⋊Q8C3×C411yescharacteristic
79C3×#121—21no—
80C3×#121Dic311yescharacteristic
81C3×#121C3×C411yescharacteristic
82C3×C4×Q8—21no—
83C3×C4×Q8C2×D311yescharacteristic
84C3×C4×Q8C22×C311yescharacteristic
85C3×C4×D4—22no—
86C3×C4×D4—21no—
87C3×C4×D4—21no—
88C3×C4×D4—21no—
89C3×C4×D4C2×D311yescharacteristic
90C3×C4×D4C22×C311yescharacteristic
91C3×#117—22no—
92C3×#117—21no—
93C3×#117—21no—
94C2×C3×C42—21no—
95C2×C3×C42C2×D311yescharacteristic
96C2×C3×C42C22×C311yescharacteristic
97C2×#208—21no—
98C3×C4⋊C8—32no—
99C3×C4⋊C8—61no—
100C3×C4⋊C8—61no—
101C3×C22⋊C8—61no—
102C3×C4×C8—32no—
103#830—21no—
104C4⋊(C3⋊C8)—21no—
105C4⋊(C3⋊C8)—21no—
106C4⋊(C3⋊C8)C22×C312yes—
107C4×C3⋊C8C22×C312yes—
108C23×C32—21no—
109C23×C32C22⋊C411yescharacteristic
110C32×Q8—22no—
111C32×D4—22no—
112C32×D4—42no—
113C2×C32×C4—21no—
114C2×C32×C4—21no—
115C2×C32×C4—21no—
116C2×C32×C4—22no—
117C2×C32×C4—21no—
118C2×C32×C4—21no—
119C2×C32×C4—41no—
120C2×C32×C4—41no—
121C2×C32×C4—41no—
122C2×C32×C4C22⋊C411yescharacteristic
123C2×C32×C4C22⋊C411yescharacteristic
124C2×C32×C4C22⋊C411yescharacteristic
125C2×C32×C4C22×C411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C3×C3⋊C8—42no—
129C3×C3⋊C8—42no—
130#529C3×D311yescharacteristic
131#431—31no—
132#423—31no—
133Q8⋊C8—32no—
134D4⋊C8—32no—
135C2×C3×Q8—21no—
136C2×C3×Q8C2×Dic311yescharacteristic
137C2×C3×Q8C2×C3×C411yescharacteristic
138C2×C3×D4—22no—
139C2×C3×D4—21no—
140C2×C3×D4—21no—
141C2×C3×D4—21no—
142C2×C3×D4C2×Dic311yescharacteristic
143C2×C3×D4C2×C3×C411yescharacteristic
144C22×C3×C4—22no—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—21no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4C2×Dic311yescharacteristic
151C22×C3×C4#6711yescharacteristic
152C22×C3×C4#6711yescharacteristic
153C22×C3×C4C2×C3×C411yescharacteristic
154C22×C3×C4C3×D411yescharacteristic
155C22×C3×C4C3×D411yescharacteristic
156C3×M16—122no—
157C2×C3×C8—62no—
158C2×C3×C8—62no—
159C3×C4⋊C4—22no—
160C3×C4⋊C4—22no—
161C3×C4⋊C4—22no—
162C3×C4⋊C4—22no—
163C3×C4⋊C4—21no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4—21no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4C2×Dic311yescharacteristic
174C3×C4⋊C4C2×Dic311yescharacteristic
175C3×C4⋊C4C2×C3×C411yescharacteristic
176C3×C4⋊C4C2×C3×C411yescharacteristic
177C3×C22⋊C4—22no—
178C3×C22⋊C4—22no—
179C3×C22⋊C4—22no—
180C3×C22⋊C4—22no—
181C3×C22⋊C4—22no—
182C3×C22⋊C4—21no—
183C3×C22⋊C4—21no—
184C3×C22⋊C4—21no—
185C3×C22⋊C4—21no—
186C3×C22⋊C4—21no—
187C3×C22⋊C4—21no—
188C3×C22⋊C4—21no—
189C3×C22⋊C4—21no—
190C3×C22⋊C4—21no—
191C3×C22⋊C4—21no—
192C3×C42—22no—
193C3×C42—21no—
194C3×C42—21no—
195C3×C42—21no—
196C3×C42—21no—
197C3×C42—21no—
198C3×C42—21no—
199C3×C42C2×Dic311yescharacteristic
200C3×C42#6711yescharacteristic
201C3×C42#6711yescharacteristic
202C3×C42C2×C3×C411yescharacteristic
203C3×C42C3×D411yescharacteristic
204C3×C42C3×D411yescharacteristic
205C3×C42C22×D311yescharacteristic
206C3×C42C23×C311yescharacteristic
207#208—42no—
208C2×C3⋊C8—22no—
209C2×C3⋊C8—22no—
210C22×C32—21no—
211C22×C32—21no—
212C22×C32—21no—
213C22×C32—41no—
214C22×C32—41no—
215C22×C32—41no—
216C22×C32C2×C22⋊C411yescharacteristic
217C32×C4—21no—
218C32×C4—21no—
219C32×C4—21no—
220C32×C4—21no—
221C32×C4—41no—
222C32×C4—41no—
223C32×C4—41no—
224C32×C4#13112yes—
225C32×C4AGL(1,ℤ/8)11yescharacteristic
226C32×C4#13711yescharacteristic
227C2×M16—61no—
228#126—21no—
229#125C3×Dic311yescharacteristic
230#124C3×Dic311yescharacteristic
231#123—21no—
232C22⋊Q8C3×Dic311yescharacteristic
233#121C3×Dic311yescharacteristic
234C4×Q8C2×C3×D311yescharacteristic
235C4×D4—21no—
236C4×D4C2×C3×D311yescharacteristic
237#117—21no—
238C2×C42C2×C3×D311yescharacteristic
239C4⋊C8—32no—
240C4⋊C8—61no—
241C4⋊C8—61no—
242C22⋊C8—61no—
243C4×C8—32no—
244C23×C3—22no—
245C23×C3—21no—
246C23×C3—21no—
247C23×C3—21no—
248C23×C3#21711yescharacteristic
249C23×C3C3×C22⋊C411yescharacteristic
250C3×Q8—22no—
251C3×Q8—22no—
252C3×Q8—42no—
253C3×D4—22no—
254C3×D4—22no—
255C3×D4—42no—
256C3×D4—44no—
257C3×D4—42no—
258C3×D4—42no—
259C2×C3×C4—22no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—22no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—22no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—42no—
281C2×C3×C4—41no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—42no—
286C2×C3×C4—42no—
287C2×C3×C4—42no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4#21711yescharacteristic
293C2×C3×C4#21711yescharacteristic
294C2×C3×C4#21711yescharacteristic
295C2×C3×C4C3×C22⋊C411yescharacteristic
296C2×C3×C4C3×C22⋊C411yescharacteristic
297C2×C3×C4C3×C22⋊C411yescharacteristic
298C2×C3×C4C22×Dic311yescharacteristic
299C2×C3×C4C2×#6711yescharacteristic
300C2×C3×C4C2×#6711yescharacteristic
301C2×C3×C4C22×C3×C411yescharacteristic
302C2×C3×C4C2×C3×D411yescharacteristic
303C2×C3×C4C2×C3×D411yescharacteristic
304C3×C8—122no—
305C3×C8—122no—
306C3⋊C8—42no—
307C3⋊C8—42no—
308C2×C32—41no—
309C2×C32—81no—
310C2×C32#40811yescharacteristic
311C2×C32#41711yescharacteristic
312C2×C32#42111yescharacteristic
313C2×Q8C2×C3×Dic311yescharacteristic
314C2×D4—21no—
315C2×D4C2×C3×Dic311yescharacteristic
316C22×C4—21no—
317C22×C4C2×C3×Dic311yescharacteristic
318C22×C4C3×#6711yescharacteristic
319C22×C4C3×#6711yescharacteristic
320M16—122no—
321C2×C8—62no—
322C2×C8—62no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4C2×C3×Dic311yescharacteristic
328C4⋊C4C2×C3×Dic311yescharacteristic
329C22⋊C4—21no—
330C22⋊C4—21no—
331C22⋊C4—21no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C42—21no—
335C42C2×C3×Dic311yescharacteristic
336C42C3×#6711yescharacteristic
337C42C3×#6711yescharacteristic
338C42C22×C3×D311yescharacteristic
339C22×C3—22no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—41no—
348C22×C3—41no—
349C22×C3—42no—
350C22×C3—42no—
351C22×C3—42no—
352C22×C3—41no—
353C22×C3—41no—
354C22×C3—41no—
355C22×C3—41no—
356C22×C3—41no—
357C22×C3—41no—
358C22×C3C2×#21711yescharacteristic
359C22×C3C2×C3×C22⋊C411yescharacteristic
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—22no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—41no—
372C3×C4—41no—
373C3×C4—41no—
374C3×C4—41no—
375C3×C4—42no—
376C3×C4—42no—
377C3×C4—42no—
378C3×C4—41no—
379C3×C4—41no—
380C3×C4—41no—
381C3×C4—41no—
382C3×C4—41no—
383C3×C4—41no—
384C3×C4#94812yes—
385C3×C4#94911yescharacteristic
386C3×C4#95111yescharacteristic
387C3×C4C3×#13112yes—
388C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
389C3×C4C3×#13711yescharacteristic
390C32#149511yescharacteristic, complemented, Sylow
391C23—21no—
392C23C3×#21711yescharacteristic
393Q8—22no—
394D4—22no—
395D4—42no—
396C2×C4—22no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4C3×#21711yescharacteristic
406C2×C4C3×#21711yescharacteristic
407C2×C4C3×#21711yescharacteristic
408C2×C4C22×C3×Dic311yescharacteristic
409C2×C4C2×C3×#6711yescharacteristic
410C2×C4C2×C3×#6711yescharacteristic
411C8—122no—
412C8—122no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—42no—
417C2×C3—41no—
418C2×C3—41no—
419C2×C3—82no—
420C2×C3—81no—
421C2×C3—81no—
422C2×C3#523211yescharacteristic
423C2×C3#523411yescharacteristic
424C2×C3#523611yescharacteristic
425C2×C3C3×#40811yescharacteristic
426C2×C3C3×#41711yescharacteristic
427C2×C3C3×#42111yescharacteristic
428C22—21no—
429C22—21no—
430C22—21no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22C2×C3×#21711yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—41no—
440C4—41no—
441C4—41no—
442C4C3×#94812yes—
443C4C3×#94911yescharacteristic
444C4C3×#95111yescharacteristic
445C3—21no—
446C3#7175311yescharacteristic, direct product factor
447C3C3×#149511yescharacteristic, complemented
448C2—41no—
449C2—81no—
450C2C3×#523211yescharacteristic
451C2C3×#523411yescharacteristic
452C2C3×#523611yescharacteristic
subgroupG/H
centerC2×C3×C4C2×#67
commutatorC2×C3×C4C22×C3×C4
FrattiniC42C22×C3×D3
FittingC32×#529C2
socleC22×C32C2×C22⋊C4
prime radicalC32×#121C4
cosocleC3×C42C23×C3
hypercenterC3×#529D3
hypocenterC3C3×#1495
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C3×#529

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C3×#4925C2semidirect
3. C3×#4924C2semidirect
4. C3×#4535C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
7. #71753C3direct (N × H)
30. #4925C2×C3semidirect
31. #4924C2×C3semidirect
34. #4535C2×C3semidirect
35. D4⋊(C3⋊C8)C2×C3semidirect
390. C32#1495semidirect
446. C3#71753direct (N × H)
447. C3C3×#1495semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C32×#5292
C3×#49252
C3×#49242
C3×#45352
C3×D4⋊(C3⋊C8)2
C3×#14953
#717533